Capsule Networks Fundamentals.
CapsNets group neurons into capsules, namely activity vectors, where each capsule accounts for an object of one of its parts. Each element of these vectors accounts for different properties of the object such as its pose and other properties like color, deformation, etc. [1]}. The magnitude of a capsule stands for the probability of existence of that object in the image [1]}. Fig. REF  shows a standard architecture of a CapsNet with two capsule layers, PrimaryCaps and DigitCaps (also called OutputCaps).
The poses of \(L\) -th capsules \(u_i\) , called primary capsules, are built upon convolutional layers. In order to compute the poses of the capsules of the next layer \(L+1\) , an iterative routing mechanism is performed. Each capsule \(u_i\)  makes a prediction \(\hat{u}_{{j|i}}\) , thanks to a transformation matrix \(W_{ij}\) , for the pose of an upper layer capsule \(j\)
\(\hat{u}_{{j|i}} = W_{{ij}}u_{i}.\) 
